The Mets would love to sign a third baseman and get rid of a shortstop. But the Expos’ pending fire sale at the winter meetings in Nashville beginning today may slow their efforts on both fronts.

Expos GM Omar Minaya was given a directive by Major League Baseball to slash payroll, and the Mets (and 28 other teams) may be hamstrung until the Montreal situation shakes out. That won’t happen for a matter of weeks, most baseball observers concur.

The Mets have prioritized their needs as finding a replacement for Edgardo Alfonzo and finding a place to dump shortstop Rey Ordonez, whose spate of errors and poor attitude towards fans in 2002 made him a pariah.

“We’ve got to trade Rey,” a team official told The Post this week.

Two of the few potential suitors for Ordonez disappeared this week. Milwaukee signed Royce Clayton, and Baltimore pitcher Scott Erickson is rehabbing a torn labrum in his pitching shoulder.

The Mets had discussed an Erickson-for-Ordonez swap that is now dead, while the Brewers were a possible fit for Ordonez. Tampa Bay is looking for a shortstop, and there may be a match there unless Lou Piniella decides he doesn’t need another headache.

Although replacing Ordonez will be difficult, getting a third baseman is more a reality and atop the Mets’ to-do list. Norihiro Nakamura, a star in Japan, came for a visit Tuesday and left impressed. Nakamura has two six-year offers for $24.3 million in the Far East. The Mets were weighing whether to make an offer to a player who has been compared to Bob Horner in newspaper reports.

Bill Mueller is a free-agent candidate at third, and if they pass on Nakamura they could sign Mueller on the cheap. Mueller’s reputation is strong, as is his defensive ability.

Yet the third base situation is muddled because if the Mets choose to trade with Montreal – and possibly acquire a top-notch talent such as Vladimir Guerrero or Bartolo Colon – they may get stuck with Expos third baseman Fernando Tatis as well. Tatis has an expensive contract and a reputation as a pouter and a clubhouse cancer.